Top MCQs on Sorting Algorithms with Answers

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Question 1

Suppose we have an O(n) time algorithm that finds the median of an unsorted array. Now consider a QuickSort implementation where we first find the median using the above algorithm, then use the median as a pivot. What will be the worst-case time complexity of this modified QuickSort?

  • O(n^2 Logn)

  • O(n^2)

  • O(n Logn Logn)

  • O(nLogn)

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Question 2

What is recurrence for worst case of QuickSort and what is the time complexity in Worst case?

  • Recurrence is T(n) = T(n-2) + O(n) and time complexity is O(n^2)

  • Recurrence is T(n) = T(n-1) + O(n) and time complexity is O(n^2)

  • Recurrence is T(n) = 2T(n/2) + O(n) and time complexity is O(nLogn)

  • Recurrence is T(n) = T(n/10) + T(9n/10) + O(n) and time complexity is O(nLogn)

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Question 3

Quicksort is run on two inputs shown below to sort in ascending order taking the first element as pivot,

(i) 1, 2, 3,......., n
(ii) n, n-1, n-2,......, 2, 1

Let C1 and C2 be the number of comparisons made for the inputs (i) and (ii) respectively. Then,

  • C1 < C2 
     

  • C1 > C2

  • C1 = C2

  • We cannot say anything for arbitrary n

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Question 4

If we use Radix Sort to sort n integers in the range (nk/2,nk], for some k>0 which is independent of n, the time taken would be?

  • Θ(n)

  • Θ(kn)

  • Θ(nlogn)

  • Θ(n2)

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Question 5

What is the best time complexity of bubble sort(optimised)?

  • N^2

  • NlogN

  • N

  • N(logN)^2

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Question 6

In a modified merge sort, the input array is splitted at a position one-third of the length(N) of the array. Which of the following is the tightest upper bound on time complexity of this modified Merge Sort.

  • N(logN base 3)

  • N(logN base 2/3)

  • N(logN base 1/3)

  • N(logN base 3/2)

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Question 7

Which of the following sorting algorithms has the lowest worst-case complexity?

  • Merge Sort

  • Bubble Sort

  • Quick Sort

  • Selection Sort

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Question 8

Which of the following is not true about comparison-based sorting algorithms?

  • The minimum possible time complexity of a comparison-based sorting algorithm is O(n(log(n)) for a random input array

  • Any comparison based sorting algorithm can be made stable by using position as a criteria when two elements are compared

  • Counting Sort is not a comparison based sorting algorithm

  • Heap Sort is not a comparison based sorting algorithm.

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Question 9

In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. What would be the worst-case time complexity of the Insertion Sort algorithm, if the inputs are restricted to permutations of 1.....n with at most n inversions?

  • Θ (n2)

  • Θ (n*log(n))

  • Θ (n1.5)

  • Θ (n)

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Question 10

You have an array of n elements. Suppose you implement quick sort by always choosing the central element of the array as the pivot. Then the tightest upper bound for the worst case performance is

  • O(n2)

  • O(n*log(n))

  • Theta(n*log(n))

  • O(n3)

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There are 31 questions to complete.

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